In an optical communications field, digital coherent communications systems in which a coherent detection scheme of dramatically improving frequency utilization efficiency is combined with digital signal processing are attracting attention. Compared to systems constructed based on direct detection, digital coherent communications systems are known to be capable of not only improving receiving sensitivity but also compensating for waveform distortion of a transmission signal caused by chromatic dispersion and/or polarization mode dispersion resulting from optical fiber transmission by receiving the transmission signal as a digital signal, and introduction of the digital coherent communications systems as a next generation optical communications technique is being discussed.
Signal light received in a coherent receiver is multiplied by local oscillator light and converted into a baseband signal. In a laser oscillator that generates a carrier of signal light or local oscillator light, it is difficult to implement frequency stabilization by a phase-locked loop which is generally used in an oscillator for wireless communications, and a large frequency offset occurs between an output frequency of a laser oscillator of a transmitter and an output frequency of a laser oscillator of a receiver occurs. In an optical communications system, a frequency offset reaches ±5 GHz. In a coherent communications system, since information is carried on the phase of a carrier, it is necessary for a receiver to estimate and compensate for a frequency offset.
Furthermore, in wireless communications, a frequency offset occurs due to errors of oscillation frequencies of reference oscillators used in a transmitter and a receiver and the Doppler shift associated with movement of a transmitter and a receiver. Even in this case, it is necessary for the receiver to estimate and compensate for a frequency offset.
As conventional estimation of a frequency offset, there is a method using a known pilot symbol (refer to Non-Patent Document 1). However, this method has a problem in that a transmission speed is reduced because a known pilot symbol not contributing to information transmission is added to a transmission signal, and a circuit and a procedure for detecting the known pilot symbol is required.
On the other hand, as a frequency offset estimation method requiring no known pilot symbol, a method using a phase increment algorithm utilizing phase change information of a symbol in one symbol period (refer to Non-Patent Document 2) and a method utilizing a frequency spectrum (refer to Non-Patent Document 3) have been known.
FIG. 17 is a block diagram illustrating a configuration example of a conventional frequency offset estimation apparatus using a phase increment algorithm for an M-ary phase shift keying (M-PSK) modulation signal. The frequency offset estimation apparatus illustrated in FIG. 17 includes a 1-symbol delay unit 101, a complex conjugate unit 102, a multiplication unit 103, an Mth power unit 104, an addition unit 105, and a phase detection unit 106.
An input signal I+jQ is a complex signal obtained by sampling in advance a received signal with a predetermined sampling frequency. The input signal is split into two, wherein one split signal passes through the 1-symbol delay unit 101 and the complex conjugate unit 102, is multiplied by the other split signal in the multiplication unit 103, and becomes a complex signal with phase change information of one symbol. This complex signal is raised to an Mth (a positive integer) power in the Mth power unit 104, so that a phase change caused by data modulation is eliminated. Signals from which the phase change has been eliminated are added over N (a positive integer) symbols in the addition unit 105, so that averaging related to a phase is performed, resulting in the elimination of an instantaneous change. A phase is extracted from the signal after the addition in the phase detection unit 106, and a phase corresponding to M times the phase change in one symbol caused by the Mth power operation of the Mth power unit 104 is multiplied by 1/M. As a consequence, the phase change Δθ of one symbol caused by a frequency offset is obtained. An estimated frequency offset Δf is calculated by the following formula. Note that in this formula, RS denotes a symbol rate.
                    [                  Expression          ⁢                                          ⁢          1                ]                                                                      Δ          ⁢                                          ⁢          f                =                              Δθ                          2              ⁢              π                                ⁢                      R            S                                              (                  formula          ⁢                                          ⁢          1                )            
FIG. 18 is a block diagram illustrating a configuration example of a conventional frequency offset estimation apparatus using a frequency spectrum. The frequency offset estimation apparatus illustrated in FIG. 18 includes a multiplication unit 107, a fast Fourier transform (FFT) unit 108, a frequency error detection unit 109, and a numerically-controlled oscillator (NCO) unit 110.
An input signal I+jQ is a complex signal obtained by sampling in advance a received signal with a predetermined sampling frequency. The input signal is multiplied by an output signal of the NCO 110 in the multiplication unit 107, so that the frequency of the input signal is changed. The signal with the changed frequency is input to the FFT unit 108 and is converted into a frequency spectrum in a frequency domain. The frequency error detection unit 109 measures the frequency spectrum and outputs a frequency error signal. Based on this frequency error signal, the NCO unit 110 changes the frequency of its output signal in predetermined steps. The above loop operation is repeated until the frequency error signal is nearly 0, and the frequency offset estimation is completed when the frequency error signal is nearly 0 and converges.
The phase increment algorithm illustrated in FIG. 17 accurately operates only for an M-PSK modulation signal, in which constellation points are arranged at an equal phase interval on a constellation, and does not operate for a signal modulated with quadrature amplitude modulation (QAM). Frequency offset estimation methods requiring no known pilot symbol for the signal modulated with QAM are disclosed in Non-Patent Document 4 and Non-Patent Document 5. Formulas representing the estimation methods disclosed in these documents are as follows.
                    [                  Expression          ⁢                                          ⁢          2                ]                                                                      f          ^                =                              1            4                    ⁢          arg          ⁢                                    max              f                        ⁢                                          ∑                                  p                  =                  1                                2                            ⁢                                                          ⁢                                                                                                            1                      N                                        ⁢                                                                  ∑                                                  t                          =                          0                                                                          N                          -                          1                                                                    ⁢                                                                                          ⁢                                                                                                    y                            4                                                    ⁡                                                      (                                                          p                              ,                              t                                                        )                                                                          ⁢                                                  ⅇ                                                                                    -                              j2π                                                        ⁢                                                                                                                  ⁢                            ft                                                                                                                                                                2                                                                        (                  formula          ⁢                                          ⁢          2                )                            where {circumflex over (f)}: estimated frequency offset        arg max f g(x): operator for obtaining x that gives maximum value of function g(x)        
Here, y(p, t) is a received signal and is a function of polarization p and a time t. Furthermore, N denotes the number of symbols used in estimation, and RS denotes a symbol rate.
                    [                  Expression          ⁢                                          ⁢          3                ]                                                                      -                                    R              S                        2                          ≤        f        ≤                              R            S                    2                                    (                  formula          ⁢                                          ⁢          3                )            
Here, an estimation range of a frequency offset of Formula 2 is limited by Formula 3.
Next, the operation of the estimation method will be described with reference to FIG. 19 to FIG. 22.
FIG. 19 to FIG. 22 are explanatory diagrams illustrating the operation of the frequency offset estimation method according to Non-Patent Document 4 and Non-Patent Document 5.
FIG. 19 illustrates a constellation when a signal modulated with 64 QAM has a frequency offset of 0 or an integer multiple of RS/4 and a phase offset remains. The period of constellation points is a reciprocal of a symbol rate, 1/RS, and when a frequency offset is RS/4, constellation points on the constellation exist in positions rotated by exactly π/2 from positions when the frequency offset is 0. That is, the arrangement of the constellation when the frequency offset is 0 is the same as that when the frequency offset is an integer multiple of RS/4. Since a signal modulated with QAM has phase symmetry of π/2, when the phase of a constellation point is a phase θ, there are three points which have the distance from the origin that is equal to the distance between this constellation point and the origin and which have a phase difference of an integer multiple of π/2 with respect to this constellation point. In FIG. 19, these points are indicated by black circles k1 to k4. The phases β of the four black circles k1, k2, k3, and k4 are expressed by the following Formula 4.
                    [                  Expression          ⁢                                          ⁢          4                ]                                                            β        =                  θ          +                                    π              2                        ⁢                          n              ⁡                              (                                                      n                    =                    0                                    ,                  1                  ,                  2                  ,                  3                                )                                                                        (                  formula          ⁢                                          ⁢          4                )            
The phases when these signals have been raised to the fourth power are 4β and are expressed by the following Formula 5.
                    [                  Expression          ⁢                                          ⁢          5                ]                                                                                                                4                ⁢                β                            =                            ⁢                                                4                  ⁢                  θ                                +                                  2                  ⁢                  π                  ⁢                                                                          ⁢                  n                                                                                                        =                            ⁢                              4                ⁢                θ                                                                        (                  formula          ⁢                                          ⁢          5                )            
That is, when the four black circles k1, k2, k3, and k4 are raised to the fourth power, they converge on the same point on a complex plane. In the same manner, when the other points are raised to the fourth power, every four points having the same distance from the origin and having a phase difference of an integer multiple of π/2 converge on the same point on a complex plane.
FIG. 20 is a constellation diagram when the constellation points of the constellation of FIG. 19 have been raised to the fourth power. 64 points of FIG. 19 converge on 16 points in FIG. 20. These constellation points are asymmetrical to one another about a real axis (a horizontal axis) and an imaginary axis (a vertical axis) and the sum or the average of the constellation points is a value that is not 0.
FIG. 21 illustrates a constellation when a signal modulated with 64 QAM has a frequency offset that is not an integer multiple of RS/4. Constellation points having the same distance from the origin are arranged on the circumference. FIG. 22 is a constellation diagram when the constellation points of the constellation of FIG. 21 have been raised to the fourth power. Since these constellation points are symmetrical to one another about a real axis (a horizontal axis) and an imaginary axis (a vertical axis), the sum or the average of the constellation points is 0.
Formula 2 above includes the following term.
                              ∑                      p            =            1                    2                ⁢                                  ⁢                                                                        1                N                            ⁢                                                ∑                                      t                    =                    0                                                        N                    -                    1                                                  ⁢                                                                  ⁢                                                                            y                      4                                        ⁡                                          (                                              p                        ,                        t                                            )                                                        ⁢                                      ⅇ                                                                  -                        j2π                                            ⁢                                                                                          ⁢                      ft                                                                                                                2                                    [                  Expression          ⁢                                          ⁢          6                ]            
When this term is set as an evaluation function φc(f), this is an operation for raising a received signal y(p, t) to the fourth power, operating an inverse rotation operator exp(−j2πft) of a frequency f, and obtaining a time average. The operation of the inverse rotation operator exp(−j2πft) is to frequency-convert the frequency of the original signal by −f. Accordingly, when a frequency offset of the received signal y(p, t) is fo and the frequency f of the evaluation function φc(f) is not equal to 4fo+kRS (k is an integer), the evaluation function φc(f) is 0. Furthermore, when the frequency f is equal to 4fo+kRS (k is an integer), the evaluation function φc(f) has a value that is not 0.
Moreover, since the ambiguity of kRS (k is an integer) is eliminated by the limitation of the frequency offset estimation range of Formula 3, f which allows the evaluation function φc(f) to have a maximum value is calculated and is multiplied by ¼, so that it is possible to estimate the frequency offset fo.